Should immigrants who can't support themselves be asked to leave

Every year millions of indigent immigrants come here and consume billions of dollars worth of American tax money that could be used to help our own poor and elderly by using Medi-Cal, WIC, CHIP, CalFresh, public housing or other public services. 


In the past all immigrants had to have a US sponsor who would pay for any assistance they might need, or they were not permitted to enter the US.  If the person couldn't support themselves the sponsor had to pay for their ticket back home.  Those were the rules when the Statue of Liberty was erected and most immigrants came here via Ellis Island.


Now many cities that don't have enough money to care for their own homeless and seniors are being overwhelmed with indigent immigrants, and some want to change the rules so that indigent immigrants will no longer be entitled to tap into our tax funded assistance programs, and still be entitled to stay here.


Should we take care of our own citizens before we give money away to indigent foreigners?